Question

In the picture, point C is a point of tangency.815mDA=DE =

Answer 1

Since the angle at which a tangent of a circle meets a radius of the circle is 90 degrees, the triangle ACD is a right triangle and we can apply the Pythagorean theorem to find the length of side DA, which is the hypothenus, as follows:

`\begin{gathered} \text{hypothenus}^2=opposite^2+adjacent^2 \\ \end{gathered}`
`\begin{gathered} DA^2=DC^2_{}+CA^2 \\ \end{gathered}`
`\begin{gathered} DA^2=15^2+8^2=225+64=289 \\ DA=\sqrt[]{289}=17 \end{gathered}`

Thus:

`DA=17`

Now, to find the value of DE, we observe that AE is the radius of the circle which we have been given to be 8.

Thus, we have that:

`DE=DA-AE`
`DE=17-8=9`

Therefore:

`DE=9`